\(\displaystyle{2}{a}^{{2}}-{b}{c}-{9}{a}+{10}={0}\) then the range of ‘a' is? Let

diartrosiwk8o

diartrosiwk8o

Answered question

2022-03-31

2a2bc9a+10=0 then the range of ‘a' is?
Let a, b and c be real numbers such that 2a2bc9a+10=0 and 4b2+c2+bc7a8=0, then the range of ‘a' is?

Answer & Explanation

glikozyd3s68

glikozyd3s68

Beginner2022-04-01Added 16 answers

From the first equality
bc=2a29a+10
(4b)c=8a236a+40(1)
Substituting in the 2nd expression,
4b2+c29a+2a2+107a8=0
4b2+c2=2a2+16a+8(2)
Adding (1) and (2), we get
(2b+c)2=6a220a+48=2(3a210a+24)
Note that 3a210a+24>0,a
Similarly on subtracting (1) from (2), we get
(2bc)2=10a2+52a32=2(5a226a+16)
Find the range of a where 5a226a+160
This range will give the answer

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